| Date | November 2008 | Marks available | 4 | Reference code | 08N.1.sl.TZ0.1 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Consider the infinite geometric sequence \(3{\text{, }}3(0.9){\text{, }}3{(0.9)^2}{\text{, }}3{(0.9)^3}{\text{, }} \ldots \) .
Write down the 10th term of the sequence. Do not simplify your answer.
Consider the infinite geometric sequence \(3{\text{, }}3(0.9){\text{, }}3{(0.9)^2}{\text{, }}3{(0.9)^3}{\text{, }} \ldots \) .
Find the sum of the infinite sequence.
Markscheme
\({u_{10}} = 3{(0.9)^9}\) A1 N1
[1 mark]
recognizing \(r = 0.9\) (A1)
correct substitution A1
e.g. \(S = \frac{3}{{1 - 0.9}}\)
\(S = \frac{3}{{0.1}}\) (A1)
\(S = 30\) A1 N3
[4 marks]
Examiners report
This question was well done by most candidates. There were a surprising number of candidates who lost a mark for not simplifying \(\frac{3}{{0.1}}\) to 30 , and there were a few candidates who used the formula for the finite sum unsuccessfully.
This question was well done by most candidates. There were a surprising number of candidates who lost a mark for not simplifying \(\frac{3}{{0.1}}\) to 30, and there were a few candidates who used the formula for the finite sum unsuccessfully.
